Problem: The equation of a circle $C$ is $x^2+y^2+10x+8y+40 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2+10x) + (y^2+8y) = -40$ $(x^2+10x+25) + (y^2+8y+16) = -40 + 25 + 16$ $(x+5)^{2} + (y+4)^{2} = 1 = 1^2$ Thus, $(h, k) = (-5, -4)$ and $r = 1$.